Solving Linear Volterra – Fredholm Integral Equation of the Second Type Using Linear Programming Method

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Muna Mansoor Mustafaf

Abstract

In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods is produced. Finally, for more explanation, an algorithm is proposed and applied for testing examples to illustrate the effectiveness of the new technique.

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How to Cite
1.
Mustafaf M. Solving Linear Volterra – Fredholm Integral Equation of the Second Type Using Linear Programming Method. BSJ [Internet]. 18Mar.2020 [cited 3Apr.2020];17(1(Suppl.):0342. Available from: http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3427
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